How do I completely remove an image from my .blend file?
If you have an image (or other piece of data, such as a material) you can force remove all users by Shift clicking on the X next to it's name. This will "mark" the data for removal upon closing the file. 

After you force remove the data, you'll need to reopen the file in order for the data to be removed. You can do this quickly by saving the file with CtrlS and then opening it with CtrlShiftO and selecting the file.